Math classrooms around the country echo with cries of "I did so much study, but the questions on the exam were nothing like the homework!" In the corresponding staff rooms, teachers and professors shake their heads, knowing that the questions were just like the homework (if not EXACTLY the same). What is going wrong?

Most people understand there is a connection between homework and class performance: if you get behind on homework, you expect your grades to drop. However, we may not know what makes good homework. As a student or parent, it is tempting to think that quick homework is good homework - you couldn't be doing math fast if you were no good at it, right? To understand what might not be so good about quick homework, let's think about what happens when you can't do a problem: you go to your notes/book/tutor for a similar example and see how to proceed. This results in you finishing the problem quickly; in fact, you are normally just fine after you have seen the trick to getting started. Does this sound familiar? It should: it's completely logical and a good basis for study.

BUT...

The problems start when this is your ONLY form of study, because in an exam, you don't get a nudge.

It doesn't matter how good you are at completing a procedure, if you don't know where to start. The thought process of analyzing a problem and working out a plan for its solution is at least as important as being able to execute that solution. In fact, it is this very skill that makes mathematics required of so many non-quantitative college programs; the ability to break down an unfamiliar problem and build up a strategy for its solution is vital to many careers. By referring to an outside source, you take a shortcut and borrow somebody else's strategy. This is fine for laying foundations, but eventually, you will need to be able to come up with ideas of your own and formulate a plan of attack.

How?

If you want to be good at taking a math exam, you need to practice math like you're in an exam. You will have: a series of questions; no access to notes, friends, tutor, or internet; no calculator, or of limited type; a time limit. To perform well in this scenario, make sure your practice hits all these elements. You don't need to do them all at once (in fact, leave the time limit to be your ‘advanced setting') - just like fitness or playing an instrument, regular practice with gradual increments is the best path to success. Here is an outline of how you can get started incorporating exam-awareness into your everyday study:

When working a set of homework problems, do every other question on the list first, using whatever resources you need (notes, book, tutor, etc.). Once you are done - ideally in the same study session - go back to the beginning of the list. Work the remaining problems *without* any resources, except whatever calculator you are allowed to use in the exam. If you get stuck, think back to the problems you have already done, but do not LOOK back. This is where you might start to feel you are not doing 'good' homework, since thinking and getting stuck take time. But persevere! We want all the 'getting stuck' and 'making false starts' out of your system in your own time, NOT in precious exam time. Every time you try something (anything!) to tackle a problem, you are making progress learning strategies and deciding whether they are good or bad. The more practice you get doing this, the less likely you are to freeze up at the dreaded blank space on the exam paper. Being good at math isn't about immediately knowing how to do every problem; it is about having a good library of things to try, and developing judgement about which is best.

So that's it. Half your problems without help. Sounds easy, right? Of course, there are things that can make it difficult, but they will vary from person to person. This is a good place to start a conversation with your teacher or tutor on how to fine-tune to maximize YOUR performance. Whatever happens in the exam, always remember: we won't test you on something we haven't taught you! But you are going to need practice to judge when and how to best use the tools from class.